The Theorem of Corresponding States in Quantum Mechanics

We shall now consider very briefly the form of the theorem of corresponding states in quantum mechanics. This important extension is due to Byk and de Boer (cf. Hirschfelder, Curtiss and Bird [1954]. We shall need it in Ch. XVIII and XIX which are devoted to the study of isotopic mixtures. 

We shall again use here the same assumption as in 4 except for the use of the classical approximation (2.2.11) for j. Instead we now use the exact definition (2.2.3) 

The reduced energy levels Er = Erl may depend on N, on F/r (through the boundary conditions, IHV — 0 at the limits of the system) and on the parameter 

However p being an intensive variable, it can only depend on the ratio VfN. Thus finally 

This is the quantum extension of (2.4.12). The new parameter (2.5.6) is proporticmal to the inverse square root of the mass. For heavy molecules A- -0, and the classical approximation is valid. 

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States 27. 5. The Theorem of Corresponding States in Quantum Mechanics 32... 

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